ADVANCED MATH Algebra Standard

H.A.1 Relations and Functions: Evaluate, analyze, model and perform operations
on polynomial, absolute value, rational, radical, logarithmic, exponential,
algebraic, piece-wise and step functions and relations with and without
technology.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.1.1. Demonstrate an understanding of the concept of a function, use function notation, and determine whether or not a given relation is a function.
H.A.1.2. Given the graph of a relation, graph its inverse, demonstrating an understanding of the reversing roles of domain and range.
H.A.1.3 Evaluate and interpret functions.
H.A.1.4 Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function.
H.A.1.4. Determine, with and without technology, the domain and range of a relation defined by a graph, or a table of values, or a symbolic equation, including those with restricted domains.
H.A.1.5. Represent a given relation in multiple ways : as a table of values, a graph, and a symbolic equation.
H.A.1.6 Analyze the effect on the graph of a function by changing coefficients , exponents, and other parameters of the function.
H.A.1.7 Find the zeros of a function.
H.A.1.8 Determine whether a given relation is even, odd or both
H.A.1.9 Perform operations ( addition , subtraction, division and multiplication ) of functions algebraically, numerically, and graphically

H.A.2 Linear and Absolute Value Equations and Inequalities and Systems of Equations
and Inequalities: Construct and model linear and absolute value equations and
inequalities and systems of linear equations and inequalities in two and three
variables and solve them with and without technology.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.2.1 Analyze and apply various methods to graph and solve linear and absolute value equations and inequalities.
H.A.2.2 Develop and apply the basic operations and properties of matrices (associative, commutative, identity, and inverse).
H.A.2.3 Analyze and explain the reasoning used to solve systems of linear equations and inequalities in two variables via substitution, elimination , graphing, and matrix algebra.
H.A.2.4 Solve systems of linear equations with two and three variables using graphing and algebraic methods (including matrices) and interpret the solution in the appropriate context.
H.A.2.5 Graph, solve, and analyze absolute value equations and inequalities in two variables.
H.A.2.6 Interpret, analyze, and solve linear programming problems with technology.

H.A.3 Quadratic Equations and Functions: Students solve, model and interpret
quadratic equations and functions and systems of quadratic equations.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.3.1 Define, plot and compute with complex numbers and describe how the associative, commutative, and distributive properties of operations on real numbers extend to operations on complex numbers.
H.A.3.2 Complete the square to solve a quadratic equation and to develop the quadratic formula and apply this formula to the solution of quadratic equations and the interpretation of the nature of their roots.
H.A.3.3 Sketch a quadratic function’s graph without technology, and recognize the relationships between the coefficients of a quadratic function and characteristics of its graph (e.g. shape, position, intercepts, zeros, maximum, minimum, symmetry, vertex .)
H.A.3.4 Construct and solve quadratic inequalities in one and two variables and represent their solutions graphically.
H.A.3.5 Solve equations that contain radical expressions.
H.A.3.6 Solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and graphically.

H.A.4 Conic Sections: Students will identify, analyze and sketch the graphs of the
conic sections and relate their equations and graphs.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.4.1 Identify, graph, analyze and write the equations of conic sections in standard form and general form, in order to identify the conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).
H.A.4.2 Solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equations

H.A.5 Polynomials: Perform operations with polynomials and apply these
operations to analyze the graphical behavior of polynomial functions.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.5.1 Add, subtract, multiply and divide (division of polynomials by monomials only) polynomial expressions using symbolic manipulation and physical models.
H.A.5.2 Understand and apply the binomial theorem to expand binomial expressions raised to positive integer powers .
H.A.5.3 Analyze and describe graphs of polynomial functions by examining their intercepts, zeros, domain and range, and local (turning points) and global (end) behavior.
H.A.5.4 Factor polynomials completely and apply properties of exponents to transform polynomial expressions and solve polynomial equations.
H.A.5.5 Use graphing technology to find approximate solutions for polynomial equations.
H.A.5.6 Write a polynomial equation given its solutions (i.e. real and/or complex).

H.A.6 Algebraic Fractions: Simplify algebraic and complex fractions, solve
equations involving algebraic fractions, and understand negative and fractional
exponents

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.6.1 Understand and simplify expressions using properties of negative and fractional exponents.
H.A.6.2 Perform operations (i.e. addition, subtraction, multiplication, and division) on and simplify algebraic fractions and radical expressions.
H.A.6.3 Simplify complex fractions.
H.A.6.4 Solve equations involving algebraic fractions.

H.A.7 Rational and Radical Functions: Interprets, solve and graph rational and
radical equations and functions with and without technology.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.7.1 Convert between rational exponent and radical forms of expressions.
H.A.7.2 Add, subtract, multiply, divide and evaluate rational functions and simplify rational expressions with linear and quadratic denominators.
H.A.7.3 Investigate, draw and analyze characteristics of rational and radical functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.
H.A.7.4 Solve graphically, algebraically and numerically equations involving radical and rational expressions.
H.A.7.5 Use properties of radicals to solve equations and identifies extraneous roots when they occur

H.A.8 Logarithmic and Exponential Equations and Functions: Interpret, solve and
graph logarithmic and exponential equations and functions, develop and apply
laws of exponents and logarithms to perform computations with and without
technology.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.8.1 Investigate, draw and analyze characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.
H.A.8.2 Define a logarithm as a solution to an exponential equation, and recognize the inverse relationship between functions defined by logarithms and exponential expressions, showing this relationship graphically.
H.A.8.3 Describe the effects of changes in the parameters of logarithmic and exponential functions graphically.
H.A.8.4 Solve graphically, algebraically and numerically, with and without appropriate technology, equations involving exponential and logarithmic expressions.
H.A.8.5 Approximate solutions to an exponential equation, and relate the solutions to the points of intersection of the graph of the exponential equation and the graph of a horizontal line.
H.A.8.6 Develop and apply the laws of logarithms and the change-of-base formula to simplify and evaluate natural and common logarithmic expressions and to find their approximate values.

H.A.9 Sequences and Series: Analyze and evaluate sequences and series
(including but not limited to arithmetic and geometric) and fluently apply sigma
notation with and without technology.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.9.1 Define, recognize, and discriminate between arithmetic and geometric sequences and series.
H.A.9.2 Use the properties of such sequences and series to solve problems, including finding the general term and sum recursively and explicitly.
H.A.9.3 Find partial sums of arithmetic and geometric series.
H.A.9.4 Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series and apply sigma notation to describe a series.
H.A.9.5 Translate between the numeric and symbolic form of a sequence or series.
H.A.9.6 Describe limits of sequences and apply their properties to investigate convergent and divergent series; and apply sequences and series to solve problems including sums and binomial expansion.
H.A.9.7 Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio.

H.A.10 Mathematical Reasoning and Problem Solving: Students use a variety of
strategies to solve problems.

ADVANCED MATH ALGEBRA STANDARD	This standard should be an advanced math standard in the algebra strand
ADVANCED MATH ALGEBRA STANDARD	Strongly Agree	Agree	No Opinion	Disagree	Strongly Disagree
H.A.10.1 Use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, writing an equation, and working backwards.
H.A.10.2 Decide whether a solution is reasonable in the context of the original situation.
H.A.10.3 Decide if a given algebraic statement is true always, sometimes, or never (statements involving rational or radical expressions or logarithmic or exponential functions).
H.A.10.4 Use the properties of number systems and the order of operations to justify the steps of simplifying functions and solving equations.
H.A.10.5 Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.
H.A.10.6 Use counterexamples to show that statements are false.